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Estimates for all years in table 1 were made using procedures identical to those of Lampman for 1953 and Smith for 1958 so that secular changes would not be masked by variations in approach. The price paid for this consistency is about a 10-percent downward bias in the estimates. Both the 1953 and 1958 estimates were made before the Internal Revenue Service was convinced of its obligation under the Freedom of Information Act to release tapes of estate tax returns (from which identifiers had been removed). Unfortunately, the IRS destroyed machine readable data from returns filed prior to 1962 so it is impossible to redo the earlier estimates to take advantage of greater knowledge and methodological refinements now available.

III. BEST ESTIMATES OF THE DISTRIBUTION OF WEALTH AMONG PERSONS, 1972 Much of the downward bias in table 1 can be adjusted to produce "best" estimates for 1972. The adjustments are briefly described below and the reader is referred to Smith, “The Concentration of Wealth in America, 1969" for detailed explanations of the impact of each adjustment."

1. Marital status differentials in sample weights.—There are well known differentials in mortality probabilities associated with marital status, Married persons have lower death probabilities than do widowed, divorced, separated or never married persons of the same age, sex and race. About 65 percent of the sample of decedents is married. The sample weights used for the "best" estimates incorporate marital status differentials, with the net effect of increasing the estimated number and wealth of living persons with gross assets of $60,000 or more.

2. Underreporting of assets.—The data provided by the IRS are from unaudited returns. A 1949 study by Harris found auditing results in about a 10-percent increase in the value of reported assets.' Some employees of the Internal Revenue Service contend that current auditing does not pay off that highly, but they are unable to supply support for another level. It is plausible that auditing no longer increases asset value by 10 percent, but pending support for another level, we have made 10 percent upward adjustments to asset values.

3. Valuation date differences.-Two adjustments are required to bring the values of reported assets into temporal alignment. First, the law permits estates to value decedents' assets either at date of death or, alternatively, 1 year after death. The provision is intended to shield heirs in periods of declining market prices from receiving assets taxed at higher values that received. As would be expected, use of the alternate valuation date is highly correlated with downward movements of the stock market. Since the market was relatively stable from 1972 through most of 1973, only 12 percent of estates used the alternate valuation date. For those who did, the IRS provided us with both date of death and alternate date values of gross assets. For 1965 the IRS had provided us not only with alternate and date of death values of gross assets, but for specific assets as well. An analysis of the 1965 data showed that 77.7 percent of the difference in the date of death and alternate date valuations was accounted for by corporate stock, 12.2 percent was accounted for by bonds, and the remaining 10.1 percent was accounted for by miscellaneous assets. Using the 1965 findings, the difference in date of death and alternate date value of gross assets was allocated by asset type for 1972.

The second valuation adjustment has to do with the fact that estates may not file returns for several years after death. In 1973, the oldest return was for a decedent who died in 1954. After adjustment for the selection of alternate valuation dates all asset values were converted to 1972 dollars. (See appendix for price indices).

4. Lifetime transfers.--The tax code provides that lifetime gifts made in contemplation of death or with rights of revocation and transfers for less the full money's worth are constructively part of the estate for tax purposes. Gifts with

The mortality rates used by Lampman (1953) and Smith (1958) do not contain marital status differentials.

6 Smith, op. cit., 1975.

6 See A. Joan Klebba, "Mortality from Selected Causes by Marital Status," in Vital and Health_Statistics, Series 20, Nos. 8a and 8b, National Center for Health Statistics, 1970.

*C. Lowell Harris, "Wealth Estimates as Affected by Audit of Estate Tax Returns," National Tax Journal, December 1949.

* See Smith, op. cit., 1975 for a detailed description of this and other adjustments.

rights of revocation are clearly part of the wealth of the decedent for our purposes. However, gifts in contemplation of death and transfers made for less than full money's worth are owned by the donee, who has a probability of appearing in the sample. They are not appropriately includable in the estate of the donor for wealth estimations. Unfortunately, the data provided by the IRS do not differentiate among these types of transfers. We have made a crude adjustment to the data by assuming that half of the value of lifetime transfers should be considered as belonging to the estate of the decedent and the other half are simply constructively there for taxation purposes. In any event the amounts are not large, $2.7 billion out of $38.9 billion gross assets reported on all returns.

In table 2 we present our best estimates for 1972 along with comparable estimates for 1969.

TABLE 2.-SHARE OF SUPERRICH IN WEALTH OF ALL PERSONS, 1969 AND 19721

[Dollar amounts in billions]

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1 We normally define the superrich as the 4 to 5 percent of the adult population with a net worth of $60,000 on. * Preliminary national balance sheets.

Includes 54.3 percent of assets held in trust funds. * Population age 20 and over.

We refer to persons with gross assets of $60,000 or more as top wealthholders. Top wealthholders were 5.6 percent of the adult population of (age 20 and over) in 1969 and 6 percent in 1972. There are biases in estimates of top wealthholders from estate tax returns because there is substantial nonfiling by estates with gross assets under $100,000. The existence of nonfilers is well known to the IRS, but the cost of tracking them down considerably exceeds the added revenue after collaring them. For our best estimates of concentration we have chosen to work with a smaller group referred to in an earlier paper as the superrich, and defined as persons (not families) with net worth of $60,000 or more.” Many people are struck by the fact that they have numerous friends with a net worth of $60,000 or more. That says more about the people who read papers like this than about the real world. Out there, 95 percent of the people don't have a net worth of $60,000 or more in 1972.

The concentration of wealth in the hands of the superrich is arrestingly high for assets which connote economic power beyond the index of raw dollars. Looking at corporate stock, one must conclude that the superrich who own 66.7 percent

For an estimate of the expected number of returns using simulation techniques see James D. Smith, Stephen

D. Franklin and Guy H. Orcutt, "The Intergenerational Transmission of Wealth: A Simulation Experiment," forthcoming in Thomas A. Juster, "Studies in Income and Wealth," vol. 41.

10 Although the filing level is $60,000, this level provides for a personal exemption of $60,000, a marital exemption of up to 50 percent of assets bequeathed to a spouse, deductability of debts, gifts to charity, and a credit for State taxes. The tax rate starts at 4 percent. It is believed that most of the nonfilers would have zero or very low tax liabilities.

11 Smith, op. cit., 1974.

of it, potentially control all corporate assets. It can be argued, of course, that most stockholders are passive, and that many superrich are indifferent to corporate control. This simply amplifies the power of the smaller group who are not passive. Further, we are here referring to individuals as though they were independent of one another. In fact there is a certain amount of block control by virtue of the fact that many of the superrich are married to each other. More on that later.

From 1969 to 1972 the proportion of the population counted as superrich increased from 4 to 5.2 percent of the population age 20 and over and their share of the nation's personal wealth crops up from 37 percent to 43.4 percent. In part these increases reflect inflation and in part increases of the real wealth of the society. As their share of the Nation's total wealth increased, their share of specific assets also increased. Movements of some individual asset shares should not be taken too literally, particularly bonds of corporations, foreign governments and State and local governments. These bonds are a relatively small portion of all personal wealth and are at the same time very highly concentrated even among the rich. As with any sample, the sample death draws has a sampling error associated with it, and the relative magnitude of the error is likely to be greater when the estimated values are small and the assets very unevenly distributed among persons.

Although considerable interest attaches to the concentration of wealth in the upper reaches of the distribution, one would like to observe the entire distribution. This cannot be done directly from estate tax data, but to the extent that one can extrapolate such data with functional forms, the entire distribution can be estimated.

The most renown functional form for income and wealth distribution is the Pareto. Unfortunately, it does its best work where we need the least help, i.e., at the very top. It is difficult to imagine a better sample of the top of the wealth distribution than the estate tax returns. Since the Pareto is not well suited to fitting the bottom of the distribution, we can dispense with it immediately. Two forms which have some claim to fitting the entire distribution reasonably well are the log normal and the Sec h(2)." Our preliminary use of the two forms favors the log normal over the Sec h (2). However, integrating the log normal function results in lower total asset values than the national balance sheet. This was also Atkinson's experience with British data. To compare the Sec h(2) and the log normal functions, we fitted them to total assets reported in the 1962 Survey of Consumer Finances." A visual inspection of the plots in chart 1 will satisfy most observers that both give reasonable fits, but that the log normal appears to be better suited for the lower tail.

13 The log normal model of wealth distribution asserts that the log of wealth is distributed as a normal variate. The distribution function is simply: F=Ň (log W/H, (2)). Sec h is the mathematical notion for the hyperbolic secant function, one of six functions which are defined in terms of exponential funcitons, but which satisfy relations which are reminiscent of the trigonometric functions. Sec hx is defined as follows:

1

Sec AX= Cos hx

and Cos hx="ter

2

The Sec h(2) distribution function is :

+1

where w denotes wealth and Wo is a constant. The density function or the first derivative of F can be transformed to form a Sec h(2) function by making the substitution :

-=(.)

This distribution approximates the log normal in the middle ranges but has an upper tail similar to the Pareto distribution.

18 For a brief discussion of the Sec (2) and log normal applied to wealth data, see A. B. Atkinson, "The Distribution of Wealth in Britain in the 1960's—The Estate Duty Method Reexamined," in James D. Smith, "The Personal Distribution of Income and Wealth," Columbia University Press, 1975.

1- See Dorothy s. Projector and Gertrude S. Weiss, "Survey of Financial Characteristics of Consumers," Federal Reserve Technical Papers, August 1966. The data collected in these surveys are old, 1962, but they cover the full range of wealth holding units from poor to rich. They then provide means of testing how well a functional form would do if it were estimated using only a part of the distribution and were then extrapolated to estimate the remainder.

CHART 1

PERCENT OF FAMILIES HAVING NET WORTH LESS THAN SPECIFIED AMOUNTS,
SURVEY OF FINANCIAL CHARACTERISTICS OF CONSUMERS, 1962

Log Normal Distribution

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In chart 2 we have extrapolated the distribution of net wealth across the entire population using the log normal. If one is willing to accept the proposition that the wealth is distributed normally in its logs, it would appear that 70 percent of Americans had a net worth of $10,000 or less in their own names and that 24 percent had less than $1,000.

CHART 2

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PERCENT OF PERSONS WITH NET WORTH LESS THAN SPECIFIED AMOUNTS, 1972

Net Worth ($1000's)

1

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